A Jack Mormon is a person who, although once a member of the Church of Jesus Christ of Latter-Day Saints, has abandoned that set of beliefs and strictures to a greater or lesser extent.
They are the backsliders who drink and smoke and gamble and party all night long; the ones who still believe in God, just not the word as revealed to Joseph Smith; the ones who think the church left them when it forbade polygamy; the ones who no longer believe in God; the ones who are uncertain about God; the ones who follow the church's health code but not its theology; the ones who are vehemently anti-Mormon; the ones who accept some parts of Mormon principles but not others. What all Jack Mormons have in common is they were baptized as Mormons and they have left the church in some respect.
Jack Mormon - Term sometimes used to describe a member of the Church who may not attend Church meetings or keep the covenants that they have made.
Origin of the term "Jack Mormon"
After the founding of Salt Lake City by the Mormons, non-Mormons (referred to by Mormons as "Gentiles") in the surrounding area fell into two groups - those who opposed the Mormons and those who were friendly toward them. These pro-Mormon "Gentiles" were known as Jack Mormons. Around the turn of the century, the meaning of the term changed to its current meaning.
Source: Laurence Cracroft, "Confessions of a Native Utahn: Tracing Church Hierarchy from First Presidency Through Jack Mormon", Salt Lake City Tribune, May 30, 1999.
The term was coined by an anti-Masonic editor named Sharp, in western New York State. He first invented the name "Jack-Mason," to refer to people who refused to take part in the anti-Masonic movement of the time. Sharp was also anti-Mormon, and he likewise created the phrase "Jack Mormon" for those persons who, while not Mormons themselves, were opposed to the illegal procedure and mob violence advocated by Sharp and others against the Mormons.
Source: H. Clay Gorton, "Ask Gramps" column, Mormon Town Neighbor (web publication), undated.
Theory #3 - my own
The "jack" component is used as an adjective indicating something that is has the appearance of that thing, or is a corruption of that thing, such as a Jackrabbit, which is actually a hare.
Jack Mormon Trivia
Former heavyweight champion William Harrison "Jack" Dempsey chose his fighting name to reflect the fact that he wasn't a very faithful Mormon.
Source: W.H. Stickney Jr., "Manassa not ready to forget Dempsey", Houston TX Chronicle, Aug 1, 1999.
Jack Mormon Joke
A bum asks a jack Mormon for two dollars.
The man says, "If I give you the money, will you just use it to buy booze?"
The bum says no.
The man asks, "Will you gamble it away?"
The bum says no.
Then the man asks, "Then will you come home with me so my Mormon wife can see what happens to a man who doesn’t drink or gamble?"